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ⓘ Matematik India - yang dimaksudkan di sini ialah matematik yang muncul Asia Selatan sejak zaman silam hingga akhir kurun ke-18 - bermula dalam tamadun Lembah In ..



Matematik India
                                     

ⓘ Matematik India

Matematik India - yang dimaksudkan di sini ialah matematik yang muncul Asia Selatan sejak zaman silam hingga akhir kurun ke-18 - bermula dalam tamadun Lembah Indus pada Zaman Gangsa dan kebudayaan Veda pada Zaman Besi. Semasa tempoh matematik India klasik, sumbangan-sumbangan penting telah dibuat oleh sarjana-sarjana seperti Aryabhatta, Brahmagupta, dan Bhaskara II. Ahli matematik India telah membuat sumbangan-sumbangan terawal terhadap pengkajian sistem nombor desimal, sifar, nombor negatif, aritmetik, dan algebra.

Di samping itu, trigonometri yang berkembang di dunia Hellenistik dan telah diperkenalkan ke India kuno melalui terjemahan buku Yunani, berkembang lanjut di India, dan khususnya, takrifan-takrifan moden bagi sinus dan kosinus dimajukan di sana. Konsep-konsep matematik ini dipindahkan ke Timur Tengah, China dan Eropah dan membawa kepada kemajuan lebih lanjut yang kini membentuk asas-asas bagi banyak bidang matematik.

Karya-karya matematik India kuno dan Zaman Pertengahan, semuanya ditulis dalam bahasa Sanskrit, selalunya mengandungi satu seksyen sutra yang merupakan satu set peraturan-peraturan atau masalah-masalah yang dinyatakan dengan cukup cermat dalam ayat supaya dapat membantu pelajar untuk menghafaznya. Ini diikuti dengan seksyen kedua yang mengandungi ulasan prosa kadang-kala pelbagai ulasan oleh pelbagai sarjana yang menjelaskan masalah itu dengan lebih terperinci dan menyediakan hujah bagi penyelesaian. Di seksyen prosa, bentuk itu tidak dianggap sebagai penting sepertimana idea terbabit. Semua karya-karya matematik dipindahkan secara lisan sehinggalah sekitar tahun 500SM; selepas itu, semua karya itu dipindahkan secara lisan dan juga dalam bentuk manuskrip. Dokumen matematik tertua yang dihasilkan di India yang masih wujud ialah Manuskrip Bakhshali kulit kayu birch yang dijumpai pada tahun 1881 di kampung Bakhshali, berhampiran Peshawar, Pakistan; manuskrip itu kelihatan berasal dari tahun 200SM hingga 200M. Sarjana-sarjana terdahulu telah berhujah bahawa ia mungkin berasal dari tahun 700M.

Satu mercu tanda terkemudian dalam matematik India adalah perkembangan pengembangan siri bagi fungsi trigonometri sinus, kosinus dan kotangen oleh ahli-ahli matematik aliran Kerala pada kurun ke-15. Karya mereka yang luar biasa yang disempurnakan dua kurun sebelum rekaan kalkulus di Eropah, menyediakan apa yang kini dianggap sebagai contoh pertama bagi siri kuasa selain siri geometri. Bagaimana pun, mereka tidak merumuskan satu teori yang sistematik bagi pembezaan dan pengamiran, juga tiada bukti langsung bagi keputusan-keputusan mereka dipindahkan ke luar Kerala.

                                     

1. Bidang-bidang matematik India

Beberapa bidang matematik yang dikaji di India kuno dan Zaman Pertengahan termasuklah:

  • Aritmetik: Sistem perpuluhan, Nombor negatif lihat Brahmagupta, Sifar lihat Sistem Angka Hindu-Arab, sistem nombor notasi kedudukan moden, nombor-nombor titik apungan lihat aliran Kerala, teori nombor, Infiniti lihat Yajur Veda, nombor transfinit, nombor tak nisbah lihat Sulba Sutra
                                     

2. Buku-buku sumber dalam bahasa Sanskrit

  • Shukla, K. S. ed 1988, written at critically edited with Introduction, English Translation, Notes, Comments and Indexes, in collaboration with K.V. Sarma, New Delhi, Āryabhatīya of Āryabhata, Indian National Science Academy.
  • Pingree, David ed 1978, written at edited, translated and commented by D. Pingree, Cambridge, MA, The Yavanajātaka of Sphujidhvaja, Harvard Oriental Series 48 2 vols.
  • Shukla, K. S. ed 1976, written at critically edited with Introduction, English Translation, Notes, Comments and Indexes, New Delhi, Āryabhatīya of Āryabhata with the commentary of Bhāskara I and Someśvara, Indian National Science Academy.
  • Sarma, K. V. ed 1976, written at critically edited with Introduction and Appendices, New Delhi, Āryabhatīya of Āryabhata with the commentary of Sūryadeva Yajvan, Indian National Science Academy.
  • Neugebauer, Otto & David Pingree eds. 1970, written at New edition with translation and commentary, 2 Vols., Copenhagen, The Pañcasiddhāntikā of Varāhamihira.
  • Keller, Agathe 2006, written at Basel, Boston, and Berlin, Expounding the Mathematical Seed. Vol. 1: The Translation: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya, Birkhäuser Verlag, 172 pages, ISBN 3764372915.
  • Sen, S. N. & A. K. Bag eds. 1983, written at with Text, English Translation and Commentary, New Delhi, The Śulbasūtras of Baudhāyana, Āpastamba, Kātyāyana and Mānava, Indian National Science Academy.
  • Keller, Agathe 2006, written at Basel, Boston, and Berlin, Expounding the Mathematical Seed. Vol. 2: The Supplements: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya, Birkhäuser Verlag, 206 pages, ISBN 3764372923.
                                     

3. Rujukan

  • Bourbaki, Nicolas 1998, written at Berlin, Heidelberg, and New York, Elements of the History of Mathematics, Springer-Verlag, 301 pages, ISBN 3540647678.
  • van der Waerden, B. L. 1983, written at Berlin and New York, Geometry and Algebra in Ancient Civilizations, Springer, 223 pages, ISBN 0387121595
  • van der Waerden, B. L. 1988, "Reconstruction of a Greek table of chords", Archive for History of Exact Sciences 38 1: 23-38,
  • De Young, Gregg 1995, "Euclidean Geometry in the Mathematical Tradition of Islamic India", Historia Mathematica 22: 138-153.
  • Boyer, C. B. & U. C. Merzback fwd. by Issac Asimov 1991, written at New York, History of Mathematics, John Wiley and Sons, 736 pages, ISBN 0471543977.
  • Thibaut, George 1984, orig. 1875, written at Calcutta and Delhi, Mathematics in the Making in Ancient India: reprints of On the Sulvasutras and Baudhyayana Sulva-sutra, K. P. Bagchi and Company orig. Journal of Asiatic Society of Bengal, 133 pages.
  • Dani, S. G. July 25, 2003, "Pythogorean Triples in the Sulvasutras", Current Science 85 2: 219-224.
  • Singh, A. N. 1936, "On the Use of Series in Hindu Mathematics", Osiris 1: 606-628,
  • Staal, Frits 2006, "Artificial Languages Across Sciences and Civilizations", Journal of Indian Philosophy, Springer Netherlands Springer Netherlands, 34 1: 89-141.
  • Datta, Bibhutibhusan & Avadesh Narayan Singh 1962, written at Bombay, History of Hindu Mathematics: A Source Book, Asia Publishing House.
  • Bronkhorst, Johannes 2001, "Panini and Euclid: Reflections on Indian Geometry", Journal of Indian Philosophy, Springer Netherlands Springer Netherlands, 29 1-2: 43-80.
  • Bressoud, David 2002, "Was Calculus Invented in India?", The College Mathematics Journal Math. Assoc. Amer. 33 1: 2-13.
  • Staal, Frits 2001, "Squares and oblongs in the Veda", Journal of Indian Philosophy, Springer Netherlands Springer Netherlands, 29 1-2: 256-272.
  • Burnett, Charles 2006, "The Semantics of Indian Numerals in Arabic, Greek and Latin", Journal of Indian Philosophy, Springer-Netherlands Springer Netherlands, 34 1-2: 15-30.
  • Van Nooten, B. 1993, "Binary numbers in Indian antiquity", Journal of Indian Philosophy, Springer Netherlands, 21 1: 31-50,
  • Yano, Michio 2006, "Oral and Written Transmission of the Exact Sciences in Sanskrit", Journal of Indian Philosophy Springer Netherlands 34 1-2: 143-160.
  • Datta, Bibhutibhusan Dec., 1931, "Early Literary Evidence of the Use of the Zero in India", The American Mathematical Monthly 38 10: 566-572.
  • Staal, Frits 1986, written at Mededelingen der Koninklijke Nederlandse Akademie von Wetenschappen, Afd. Letterkunde, NS 49, 8. Amsterdam, The Fidelity of Oral Tradition and the Origins of Science, North Holland Publishing Company, 40 pages.
  • Burton, David M. 1997, The History of Mathematics: An Introduction, The McGraw-Hill Companies, Inc., 193-220.
  • van der Waerden, B. L. 1988, "On the Romaka-Siddhānta", Archive for History of Exact Sciences 38 1: 1-11,
  • Stillwell, John 2004, written at Berlin and New York, Mathematics and its History 2 ed., Springer, 568 pages, ISBN 0387953361.
  • Filliozat, Pierre-Sylvain 2004, ", written at Washington DC, in Gorini, Catherine A., Geometry at Work: Papers in Applied Geometry, vol. 53, pp. 46-58, Mathematical Association of America Notes, 236 pages, 46-58, ISBN 0883851644.
  • Cooke, Roger 2005, written at New York, The History of Mathematics: A Brief Course, Wiley-Interscience, 632 pages, ISBN 0471444596.
  • Staal, Frits 1999, "Greek and Vedic Geometry", Journal of Indian Philosophy, Springer Netherlands, 27 1-2: 105-127.
  • Encyclopaedia Britannica Kim Plofker 2007, "mathematics, South Asian", Encyclopædia Britannica Online: 1-12.
  • Staal, Frits 1995, "The Sanskrit of science", Journal of Indian Philosophy, Springer Netherlands Springer Netherlands, 23 1: 73-127.
  • Roy, Ranjan 1990, "Discovery of the Series Formula for π {\displaystyle \pi } by Leibniz, Gregory, and Nilakantha", Mathematics Magazine Math. Assoc. Amer. 63 5: 291-306.


                                     

4. Pautan luar

  • An overview of Indian mathematics, MacTutor History of Mathematics Archive, St Andrews University, 2000.
  • Online course material for InSIGHT, a workshop on traditional Indian sciences for school children conducted by the Computer Science department of Anna University, Chennai, India.
  • Indian Mathematics: Redressing the balance, Student Projects in the History of Mathematics. Ian Pearce. MacTutor History of Mathematics Archive, St Andrews University, 2002.
  • Index of Ancient Indian mathematics, MacTutor History of Mathematics Archive, St Andrews University, 2004.

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